Paper 2020/1310

A note on the low order assumption in class group of an imaginary quadratic number fields

Karim Belabas and Thorsten Kleinjung and Antonio Sanso and Benjamin Wesolowski

Abstract

In this short note we analyze the low order assumption in the imaginary quadratic number fields. We show how this assumption is broken for Mersenne primes. We also provide a description on how to possible attack this assumption for other class of prime numbers leveraging some new mathematical tool coming from higher (cubic) number fields.